Efficient L-Shape Fitting for Vehicle DetectionUsing Laser Scanners

Xiao Zhang†, Wenda Xu†, Chiyu Dong†, John M. Dolan†,‡

†Electrical and Computer Engineering, Carnegie Mellon University‡Robotics Institute, Carnegie Mellon University

June, 2017

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Outline

1 Introduction

2 L-Shape based Vehicle Detection

3 Experimental Results

4 Conclusions

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Introduction

• Detection of surrounding objects is an essential task inautonomous driving.

• LIDAR, laser scanner, widely used for collecting range data

• Segmentation• segment range data into meaningful cluster of points

• Feature Extraction• line segments, chunks, rectangles, L-shape, ...• walls, bicycles, woods, bushes, vehicles, pedestrians, ...

• Tracking• feature association: static map, moving targets• tracking: Extended Kalman Filter(EKF), Rao-Blackwellized

Particle Filter (RBPF)

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Related Work

• CMU’s “Boss”, won DARPA Urban Challenge in 2007• urban environment, low-density and low-speed traffic• merging, passing, interacting with manned/unmanned vehicle• 3D LIDAR sensors sitting on top, e.g. Velodyne HDL-64• high-definition, but expensive

• CMU’s new Cadillac SRX research platform• production-grade sensors, e.g. IBEOs• reduce equipment expenditure, enable a neat appearance

Figure: CMU’s new autonomous vehicle research platform “SRX”

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Related Work

• Challenges• giving up high-definition dense range points in 3D• detect only object’s contour that face towards sensor in 2D

• Relevant Work• Principal Component Analysis (PCA)1

• weighted least squares: line fitting + corner fitting2

• utilize scanning order info to split cluster into two edges3

• L-Shape based Vehicle Detection• no need for laser scanning sequence information• robust to various range point density• flexible to accommodate specified fitting criterion• effectiveness demonstrated by experiments

1Huijing Zhao, Quanshi Zhang, Masaki Chiba, et al. “Moving object classification using horizontal laser scandata”. In: IEEE International Conference on Robotics and Automation. 2009, pp. 2424–2430.

2Robert MacLachlan and Christoph Mertz. “Tracking of moving objects from a moving vehicle using a scanninglaser rangefinder”. In: IEEE Intelligent Transportation Systems Conference. 2006, pp. 301–306.

3Xiaotong Shen, Scott Pendleton, and Marcelo H Ang. “Efficient L-shape fitting of laser scanner data forvehicle pose estimation”. In: IEEE Conference on Robotics, Automation and Mechatronics. 2015, pp. 173–178.

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Outline

1 Introduction

2 L-Shape based Vehicle Detection

3 Experimental Results

4 Conclusions

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Segmentation• divide the range points into clusters according to an adapting

threshold• K-D tree data structure for finding neighboring points within

distance threshold• further speedup if scanning order available

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Minimize Least Squares in L-Shape Fitting• optimization problem

• L-Shape rectangle model assumption• least squares - classical fitting criterion

minimizeP,θ,c1,c2

∑i∈P

(xi cos θ + yi sin θ − c1)2

+∑i∈Q

(−xi sin θ + yi cos θ − c2)2

subject to P ∪Q = {1, 2, ...,m}c1, c2 ∈ R 0◦ ≤ θ < 90◦

(1)

• decision variables• optimal disjunction (P,Q) split the m points into two sets• optimal parameters (θ, c1, c2) for two perpendicular lines

• the two line expressions• x cos θ + y sin θ = c1 and −x sin θ + y cos θ = c2

• difficult optimization problem• combinatorial complexities due to partition

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Search-Based Rectangle Fitting

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Search-Based Rectangle Fitting

• iterate through all possible headings (θ) of the rectangle• at each heading θ

• find the smallest rectangle oriented at θ which covers thiscluster of points

• obtain projections to rectangle edges for all points• split points into P and Q according to these distances• obtain the fitting criterion

• select optimal heading which achieves the best fitting criterion10 / 20

Fitting Criterion

• Area Minimization• minimize rectangle area• looking for the smallest rectangle that covers all the points

• Closeness Maximization• maximize points-to-edges closeness• emphasize how close these range points are to the 2-D contour

facing towards the sensor

• Variance Minimization• minimize points-to-edges squared error• emphasize the squared error of the two orthogonal edges fitted

by the two disjoint groups of points• actually looking for an approximated solution to the above

optimization problem

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Outline

1 Introduction

2 L-Shape based Vehicle Detection

3 Experimental Results

4 Conclusions

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Typical Rectangle Fitting Example

x (m)-11 -10 -9 -8

y (m

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a Fitted rectangle.

Theta (deg)0 30 60 89

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AreaClosenessVariance

b Fitting criterion.

Figure: In example (a), the fitting results from the three criteria are very similar, andthe maxima of the three curves in (b) are very close (marked by arrows and achievedat 88◦, 89◦, and 0◦, respectively).

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Heading Accuracy in Rectangle Fitting

• Observations• dataset (145), headings manually labeled at resolution 1◦

• closeness maximization and variance minimization have veryhigh correctness, better than PCA

• area minimization is only guaranteed with dense range points,e.g. small object or more powerful LIDAR

Real Error (θ − θg) Absolute Error (|θ − θg|)Method Mean (deg) STD (deg) Mean (deg) STD (deg)

PCA -5.60 10.68 10.09 6.57

Area 0.65 14.80 11.78 8.46

Closeness 0.01 3.65 2.47 3.36

Variance -0.15 2.19 1.55 1.66

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Heading Error Histogram

Heading error (deg)-30 -20 -10 0 10 20 30

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40Heading Error Histogram

for PCA

Heading error (deg)-30 -20 -10 0 10 20 30

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40Heading Error Histogram

for Area Criterion

Heading error (deg)-30 -20 -10 0 10 20 30

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40Heading Error Histogramfor Closeness Criterion

Heading error (deg)-30 -20 -10 0 10 20 30

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40Heading Error Histogram

for Variance Criterion

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Example by Minimize Area Criteria Fitting

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a Fitted rectangle.

Theta (deg)0 30 60 89

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b Fitting criterion.

Figure: In example (a), the fitting result from the area criteria is different from theother two, and its maximum in (b) is away from the other two (achieved at 69◦, 1◦,and 86◦, respectively).

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Fitting Results for Typical Cycles

a Camera view.

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VarianceClosenessArea

b Vehicle fitting results.

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Fitting Results for Typical Cycles

a Camera view.

b Vehicle fitting results.

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Computation Efficiency

• Observations• dataset: 10k laser scans collected on local roads• MATLAB, Linux, Intel Core i7 CPU• variance minimization criterion is the most time-consuming,

due to heavy computation in calculating the variance

Criterion Mean (ms) STD (ms)

Area Minimization 3.56 0.19

Closeness Maximization 4.00 0.23

Variance Minimization 8.37 0.32

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Conclusions

• A search-based L-Shape fitting approach for vehicle detection• no need for the scan ordering information, enabling fusion of

raw laser data from multiple laser scanners• computationally efficient and easy to implement, involving very

few parameters and no need for hands-on experience orparameter tuning

• accommodate any specified criterion, flexible for differentfitting demands

• effective and robust (criterion Closeness and Variance),demonstrated by on-road experiments with production-gradesensors

• Future work• improve the algorithms to be more robust with outliers, e.g.

SUV side mirrors• compare headings through successive cycles

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